Yes it depends on the way you handle the response of the CRC, you could say "give me the data I don't care" or "please try to read it again it's wrong".

In my opinion that is just the proof that it's not as simple as "it just works or not" but rather : depending on muptiple factors such as error correction and the way your algorithm works on the receiver it may "half work" no matter what kind of cable you plug in.